{"product_id":"discrete-series-of-gln-over-george-lusztig-9780691081540","title":"Discrete Series of Gln Over a Finite Field","description":"\u003cp\u003eIn this book Professor Lusztig solves an interesting problem by entirely new methods: specifically, the use of cohomology of buildings and related complexes. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003eThe book gives an explicit construction of one distinguished member, D(V), of the discrete series of GLn (Fq), where V is the n-dimensional F-vector space on which GLn(Fq) acts. This is a p-adic representation; more precisely D(V) is a free module of rank (q--1) (q2--1)...(qn-1--1) over the ring of Witt vectors WF of F. \u003cp\u003e\u003c\/p\u003e In Chapter 1 the author studies the homology of partially ordered sets, and proves some vanishing theorems for the homology of some partially ordered sets associated to geometric structures. Chapter 2 is a study of the representation △ of the affine group over a finite field. In Chapter 3 D(V) is defined, and its restriction to parabolic subgroups is determined. In Chapter 4 the author computes the character of D(V), and shows how to obtain other members of the discrete series by applying Galois automorphisms to D(V). Applications are in Chapter 5. As one of the main applications of his study the author gives a precise analysis of a Brauer lifting of the standard representation of GLn(Fq).\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e George Lusztig\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 0691081549\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9780691081540\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Princeton University Press\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 10\/21\/1974\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 104\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.30lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.24h x 6.14w x 0.32d","brand":"George Lusztig","offers":[{"title":"Paperback","offer_id":48086764847359,"sku":"9780691081540","price":75.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_349beb88-07db-48f7-ad75-b1b6e8d79e29.jpg?v=1769096443","url":"https:\/\/www.whiterainbookhouse.com\/products\/discrete-series-of-gln-over-george-lusztig-9780691081540","provider":"WR Book House","version":"1.0","type":"link"}